When referring to job responsabilities, the work "task" is much more common.
According to Sana's definition, the word "errand" would normally be used if you have to leave the office for something, like to deliver something to a client, or go buy some office supplies.
Even in that case, "running an errand" could be considered a "task".
Also, we use different verbs in association with each of those words, for example:
You "perform a task".
You "run an errand".